Heat olive oil in an 11-inch skillet over medium heat.

Add the diced potato, sliced onion, and chopped green beans to the skillet.

Cover the skillet and cook, stirring occasionally, until the vegetables soften (approximately 10-15 minutes).

In a large bowl, lightly whisk the eggs.

Whisk in the basil pesto and finely chopped fresh basil into the eggs.

Pour the egg mixture evenly over the cooked vegetables in the skillet.

Sprinkle the grated Parmesan cheese evenly over the egg mixture.

Cook the frittata, uncovered, over low heat until the eggs are almost set (approximately 10-15 minutes).

Preheat the broiler to high.

Place the skillet under the broiler, shielding the handle with foil if necessary.

Broil until the cheese is melted and lightly browned (approximately 2-3 minutes).

Remove the frittata from the broiler and let it stand for 10 minutes before serving.